David,
A couple of years ago I was at the local farm and ranch store and they had a sale on solid "rubber" stall mats. I don't know what kind of rubber they actually are. They are about 3ftX4ft (they had larger ones as well) and 3/4 of an inch thick. They may have been made from recycled tires. I bought one as a backstop for my bag and 3-D targets and they work great. I think it cost me 50 bucks.
After about 6 months of having it flop around all over the place when I would shoot, I built a cheap 2X4 frame for it. I put 4 big brass grommets across the long edge and hung it on hooks I screwed into the board across the top. I think I spent a total of 30 bucks on lumber and hardware.
The frame has two feet perpendicular to the frame where the mat hangs so it is sturdy. The mat is pretty heavy so I wouldn't really call it portable unless you have a couple of buddies to help, but target points barely puncture and a broad head doesn’t penetrate past the base of the ferrule. It is slightly "self healing" but I wouldn't shoot broad heads right into it as a habit.
Our local farm and home is an Atwood's, but I bet you can find them just about anywhere.
OkKeith